With Senate Republicans standing firm against the measure, the friendly fire from Democrats means there’s only more work ahead as Lieberman and others scramble to cobble together 60 votes to move the bill.

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A handful of members, including Sens. Al Franken of Minnesota and Richard Blumenthal of Connecticut, are echoing the concerns of civil liberties groups, which are growing increasingly fearful that consumers’ data could end up being passed around by companies and the government as security experts share with each other information about emerging cyberthreats.

To them and others, the Senate measure as written would specify too few limitations on how data could be used and cover entities with too broad a protection from liability.

“I have serious concerns about this bill,” Franken told POLITICO in a statement. “As written, the legislation moves aside decades of privacy laws to allow companies to freely monitor American citizens’ communications and give their personal information to the federal government — and grants companies near total immunity for doing so.”

Lieberman and his allies are already fighting on another front to build a 60-vote supermajority for the bill: They’re trying to court Republicans, some of whom are skeptical of the measure’s key provision to require critical infrastructure — for instance, some water plants and power systems — to secure their systems.

But the bill’s information-sharing provisions are just as important, and they’re triggering vocal consternation among privacy hawks both on and off Capitol Hill. The ACLU, Center for Democracy & Technology, FreedomWorks, Americans for Limited Government and a handful of other groups wrote senators on Thursday to urge opposition to the current version of Lieberman’s bill. The missive could serve to drum up more support, including from Democrats, to alter the bill.

For now, supporters say they’re listening. A spokeswoman for Lieberman on the Senate Homeland Security and Governmental Affairs Committee said Lieberman and his allies have “long been discussing possible revisions to strengthen privacy and civil liberty provisions.” Civil liberties groups have been part of those talks, the aide said.